PHYSICAL REVIEW RESEARCH 3, 033262 (2021)

Electron transport in a nanowire irradiated by an intense laser pulse

J. F. Ong ,* P. Ghenuche ,† and K. A. Tanaka ‡

Extreme Light Infrastructure-Nuclear Physics (ELI-NP), “Horia Hulubei” National Institute for Physics and Nuclear Engineering(IFIN-HH), 30 Reactorului Street, RO-077125 Bucharest-Magurele, Romania

(Received 25 February 2021; accepted 31 August 2021; published 17 September 2021)

Electron transport in a nanowire exhibits a distinct behavior following the irradiation of intense laser pulse.Using particle-in-cell simulation, we observe a large-amplitude particle-driven wakefield excitation followedby electron acceleration in the solid density. Besides, we observed the quiver of the electrons across thenanowire under the action of the surrounding laser electric field facilitating deeper wakefield propagation inthe nanowire with 2.5× energy gain over a flat target. These results open insights into the laser-energy couplingwith nanostructure targets and radiation sources, and motivate the wakefield acceleration in solid density plasma.

DOI: 10.1103/PhysRevResearch.3.033262

I. INTRODUCTION

The interaction of high-power lasers with nanostructuretargets received a lot of attention lately due to their increasedlight-matter coupling efficiency [1–4]. A laser pulse of rela-tivistic intensity can heat a nanowire target to a much largerdepth over a flat solid target [5]. Such an efficient laser energyabsorption opens up various applications such as enhancedion acceleration [6], attosecond bunch generation [7,8], en-hanced x-ray [9–13], and gamma-ray generation [14], as wellas efficient microfusion [5,15,16]. Therefore, understandingthe electron dynamics and transport in the nanostructure isfundamental for the control of these applications.

Numerous studies were carried out to investigate the elec-tron transport in the nanowires. The fast electrons generatedupon laser irradiation are collimated in the nanowire arraysfor a long time by the resistive magnetic field, typically inthe time frame of picosecond as reported in Ref. [17]. Thelaser energy absorption was mainly attributed to the vacuumheating through the laser electric field normal to the nanowiresurfaces [18,19] and was utilized to optimize the electronacceleration [20].

Typically, the electron acceleration and transport in thenanowire occur in different stages. The electric field of thelaser tears off electrons from the surface of the nanowire andaccelerates them in the forward direction by the magneticfield, forming electron bunches outside the nanowire. Thesebunches introduce a return current at the skin layer to fulfillthe requirement of local current neutrality [21]. The return

*jianfuh.ong@eli-np.ro†petru.ghenuche@eli-np.ro‡kazuo.tanaka@eli-np.ro

Published by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.

current generates a quasistatic azimuthal magnetic field thatpinches the nanowire radially inward. This nanoscale Z pinchis capable of forming an ultradense electron bunch, surpassing1000 times the critical density [15]. The laser continues topropagate in the space between the wires and heats the plasmauntil the nanowire blowout fills the space completely. Untilnow, the electron dynamics in the nanowire which contributedto the high laser energy absorption have not been addressedin detail and demand further clarification. Since real-timeobservation of electron transport across the nanowire is ex-perimentally difficult, it is of critical importance to understandelectron transport by using numerical simulation with a highspatial and temporal resolution to identify the absorptiondynamics.

In this paper, the electron dynamics accounted for the en-hanced laser energy absorption of a nanowire irradiated byintense laser pulse are reported. Particle-in-cell (PIC) simula-tions show that a wakefield is excited by the 2ωL fast electronbunches generated by the J × B mechanism at the tip of thenanowire. This wakefield has an amplitude of the order ofTV m−1, oscillating at the plasma frequency and propagatesdeep into the nanowire. Electrons injected at the later stage areaccelerated by the wakefield when the right initial conditionsare satisfied. The laser fields then brush up the side sur-faces and swing the electron across the nanowire. Theseelectrons assist the wakefield to propagate deeper into thenanowire with 2.5× energy gain over a flat target.

II. METHODS

The simulations were performed using two-dimensional(2D) PIC code EPOCH [22]. The simulation box is dis-cretized by 4069 × 256 cells with the spatial resolution �x =1.97 nm, �y = 7.81 nm, and a temporal resolution �t =3.16 as. The grid sizes are small enough to resolve the plasmawavelength λp at 1000ncr, which is ∼25 nm. Here, ncr is thecritical density. Each cell consists of ten macroparticle ionspecies. Field ionization and mobile ion are implemented,but collisional ionization is not included. The fifth order

2643-1564/2021/3(3)/033262(6) 033262-1 Published by the American Physical Society

J. F. ONG, P. GHENUCHE, AND K. A. TANAKA PHYSICAL REVIEW RESEARCH 3, 033262 (2021)

FIG. 1. (a) Snapshot of the current density Jx at t = 13 fs. Thelaser pulse travels from left to right. Electrons are stripped off fromthe surface of the nanowire and moved to the right, indicated by theforward current (blue). The return current (red) is created at the sur-face of the nanowire. A plasma wave is excited inside the nanowireas indicated by the sinusoidal current density. (b) The longitudinaldensity perturbation δne/n0 (solid line) and wakefield Ex (dashed linein normalized unit) at y = 0. Here, n0 = 60ncr is the average electrondensity created by the field ionization along the nanowire. (c) Thefrequency spectrum associated with the current density shown in (a).The dashed line indicates the plasma frequency of ωpe = 7.75ωL.

particle shape function and the current smoothing are used tosuppress the numerical heating. The laser pulse is modeledas a linearly polarized plane wave with the central wave-length λL = 0.8 μm and a peak intensity I0 = 1022 W cm−2

(a0 = 68), simulating the conditions available at ELI-NP [23].The laser is irradiated onto the nanowire at normal incidence.Here, a0 = eE0/(mcωL) is the normalized laser amplitude,where E0 is the peak laser field strength, ωL = 2π/λL is lasercentral frequency, and e and m are the charge and mass of elec-tron. The laser temporal profile is a(t ) = a0 exp[−(t − t0)2/

τ 2L ] with τL = 13.2 fs (22 fs full width at half maximum),

and t0 = 2τL. A carbon nanowire with length L = 5 μm anddiameter d = 300 nm is placed horizontally at the center ofthe simulation box. The carbon nanowire has a steplike profilewith density 0.52 g cm−3 (ni = 15ncr). The initial charge stateof the carbon atoms is zero.

III. RESULTS AND DISCUSSIONS

A. 2D PIC simulation results

The current density Jx = −enevx at t = 13 fs after laserirradiation is illustrated in Fig. 1(a). The laser first ionizesthe carbon atoms at the surface of the nanowire. Then, theEy component of the laser field strips off electrons and accel-erates them forward by the Bz component. A return currentis then generated on the surface of the nanowire to main-

tain the current quasineutrality, where the forward currentis negative (blue) and the return current is positive (red).In addition, the electron displacement from the plane of thenanowire tip (x � 1 μm) is observed. This is caused by theJ × B heating [24] due to the oscillating term of the pon-deromotive force of the linearly polarized laser field incidentnormally on the target. Details of the acceleration and elec-tron bunching mechanism outside the nanowire have beendiscussed in Refs. [7,8]. Hereafter, we focus on the electronbehavior inside the nanowire. A sinusoidal current insidethe nanowire is generated soon after laser irradiation [seeFig. 1(a) and Supplemental Material (SM) Video 1 [25]].This current has an amplitude of around | jx| = 0.4 MA/μm2,which corresponds to a current of 28 kA considering thearea of the nanowire with diameter d . The electron velocityderived from this current density has a value of vx ∼ 0.08c.The electric field component Ex and the density perturba-tion δne/n0 = ne/n0 − 1 are shown in Fig. 1(b). The constantn0 = 60ncr is the average electron density created by fieldionization along the nanowire. However, the maximum den-sity at the plane of the nanowire tip is ne = 3n0 = 180ncr

due to the compression caused by the laser radiation pres-sure. The relativistic effects of the present laser intensityincrease the cutoff density for the laser penetration up to

n′cr = 48ncr (n′

cr = γ ncr, γ =√

1 + a20/2). The nanowire is

opaque to the laser field even under self-induced transparencycondition, and hence rules out the penetration of the laser fieldinto the nanowire. In conjunction with the density, Ex hasa peak of approximately 2.4 TV m−1, which corresponds toeEx/(mcωL) ≈ 0.6. This nanoscale charge separation field is10× larger in magnitude and a thousand times smaller in scalethan the one that can be achieved by a typical laser wakefieldacceleration in an underdense plasma. Further analysis of thecurrent density spectrum gives a spike at plasma frequencyωpe = ωL

√n0/ncr = 7.75ωL as shown in Fig. 1(c). Together

with the large amplitude Ex, these signs point towards thewakefield excitation by a driving force inside the nanowire.

The driving force for the wakefield excitation is attributedto the electron bunches generated by the J × B heating at thenanowire tip. Typically, electron bunches generated in thisway are separated by 0.5λL interval or at 2ωL frequency asevident in Fig. 2. They are accelerated into the nanowire withlarge forward momentum px/(mc) ∼ 20. Due to the smalldiameter of the nanowire, these bunches are not clearly vis-ible from the current density. The longitudinal momentum ofthe bulk electrons shown in the inset of Fig. 2 exhibits awavelike structure with the amplitude ≈0.08, consistent withthe electron velocity derived earlier. The peak-to-peak intervalis the plasma wavelength λp = 2πvp/ωp ≈ 100 nm, wherevp = 0.97c is the plasma wave phase velocity. Note that thephase space in Fig. 2 is restricted to −0.1 μm � y � 0.1 μm,such that electrons in the transverse skin layer and thoseoutside the nanowire are excluded.

To understand better the electron transport in the nanowire,we present the electron macroparticles for the energyE/(mc2) = γ � 2 and the Ey component of the electric fieldin Fig. 3(a). The 2ωL electron bunches can now be readilyobserved inside the nanowire. We noticed that part of theelectrons stripped off by the laser Ey component during the

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ELECTRON TRANSPORT IN A NANOWIRE IRRADIATED … PHYSICAL REVIEW RESEARCH 3, 033262 (2021)

FIG. 2. Longitudinal electron phase space at t = 13 fs, demon-strating the presence of 2ωL electron bunches inside the nanowire.The phase space is restricted at −0.1 μm � y � 0.1 μm to excludeelectrons in the skin layer and outside the nanowire. The inset showsthe enlarged phase space for 2 μm � x � 3 μm with the plasmawavelength λp ≈ 100 nm.

first half cycle are pushed back to the nanowire at the sec-ond half cycle, similar to the vacuum heating mechanism[18,19,26]. A considerable amount of electrons right behindeach main bunch are returning to the nanowire [see the SMfor Video 1 and Fig. S1(a) [25]]. Vacuum heating is an ef-ficient absorption mechanism when the electron oscillationamplitude is larger than the preplasma length. However, adetailed analysis of the electron trajectories shown in Fig. 3(a)

FIG. 3. (a) Snapshot of electron macroparticles with γ � 2 att = 13 fs. Electrons outside the nanowire move in the +y directionwhen Ey < 0 and in the −y direction when Ey > 0, respectively. The2ωL electron bunches inside the nanowire propagates in the forwarddirection. The solid, dashed, and dash-dotted lines indicate threetrajectories of three sample electrons until t = 20 fs. (b),(c) The γ

of the corresponding electrons in (a). The arrows in (a) indicate theelectrons entering the nanowire boundary and their corresponding γ

in (b). The dashed white line indicates the boundary of the nanowireof diameter d .

FIG. 4. Electron energy spectra at t = 20 fs for nanowire (solidline) and flat target (dashed line) within the region −0.1 μm� y � 0.1 μm.

(solid and dashed lines) reveals that the electron is swingingacross the nanowire with an oscillating amplitude much largerthan the nanowire dimension itself. The electron oscillationamplitude is now yosc = a0c/ωL > d , pointing to a laser en-ergy absorption mechanism different from vacuum heating.This is nothing but a relativistic electron motion in an electro-magnetic plane wave with no net energy gain unless severalassumptions are violated, for instance, limiting the interactionregion and introducing static electric or magnetic fields asdiscussed in Ref. [26]. In the present case, there is a wake-field Ex inside the nanowire [see Fig. 2(b)], and a quasistaticmagnetic field at the boundary induced by the return current.The entering electrons (i.e., supplied by the laser electric field,Ey) pointed by the arrows in Fig. 3(a) are mostly located atEx ≈ 0, leading to the motion with constant γ as evidencedin Fig. 3(b). Some electrons can surf with the wake wave butdo not have sufficient time to be accelerated before exitingthe nanowire. Outside the nanowire, the electron gains andloses energy depending on its position in the laser phase, e.g.,the energy is zero at its maximum amplitude. In general, theenergy of the electron is locked only when it is inside thenanowire.

On the other hand, the electron generated by the J × Bheating at the tip is continuously injected into the nanowire.These electrons are shown by the dash-dotted line in Fig. 3(a),and their corresponding normalized energy is shown inFig. 3(c). The energy of the electrons that enter the nanowire isγ ∼ 8 and then drops to γ ∼ 6 after propagating for 1.8 μm.The energy then increases gradually to γ ∼ 10. The wakefieldis responsible for the electron acceleration as it is the onlylongitudinal electric field inside the nanowire.

To compare the electron energy gain inside the nanowireover a flat target, the electron energy spectra are taken att = 20 fs are shown in Fig. 4. Beyond this point, the nanoscaleZ pinch begins and leads to the collapsing of the wakefield. Inaddition, the ion response time scale to the wakefield, 2π/ωpi

at n0 is also about ∼20 fs. Here, ωpi is the ion plasma fre-quency. Therefore, the electron energy spectrum is recordedup to this point to minimize the effects of pinching andion response. For a fair comparison, the energy spectra arerestricted to −0.1 μm � y � 0.1 μm in nanowire and flattarget. The energy spectra show similar enhancement to the

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J. F. ONG, P. GHENUCHE, AND K. A. TANAKA PHYSICAL REVIEW RESEARCH 3, 033262 (2021)

FIG. 5. The current density at t = 20 fs for (a) nanowire, and(b) flat target. Both targets have the same length. The energy spectraare calculated for the region between the green lines. The arrowsindicate the physical processes with the terms used in the text.

measurements reported in Refs. [1,27]. The total electron en-ergy inside the nanowire is evaluated to be 16 and 6.4 mJ/μmfor the flat target. Generally, the nanowire overcomes the flattarget about 2.5× in electron energy gain. This is because theamplitude of the wakefield attenuates with distance into thetarget due to the velocity dispersion of the 2ωL bunches andthe interaction with the wake induced within the bunch itself[28]. But in the nanowire, the energetic entering electrons actas a drive bunch, continuously exciting the wakefield duringthe nanowire crossing and lead to the extended propagation inthe nanowire over a flat target by 1.5 μm as shown in Fig. 5.This subsequently results in enhanced energy absorption. Inaddition, the cutoff electron energy for the nanowire caseis almost double the flat target. The collisional damping ofthe wakefield was reported in Ref. [29] as a possible sourceof heating, however, the inclusion of collisional effects (bi-nary collision and collisional ionization) did not affect theresults (see the SM for Fig. S2 [25]). The low Z carbon

FIG. 6. 3D simulation results with PICONGPU code for linearly polarized laser field at t = 13 fs. (a) The isosurface of electron density atne = 4ncr . (b) The frequency spectrum associated with the longitudinal current density Jy. (c) The longitudinal electron phase space insidethe nanowire. (d) The current density components, Jy taken at z = 1 μm. (e) The longitudinal density perturbation (solid line) and wakefield(dashed line) along the nanowire center. (f) The total electron energy spectra at t = 20 fs with the one inside the nanowire. (g) The transversecurrent components. (h) The transverse current density Jx where the dashed boxes indicate the returning electron that will cross the nanowirewith the corresponding transverse momentum, px/(mc) in (i). (j) The transverse momentum component pz/(mc).

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plasma suggests that the radiation cooling time exceeds thehydrodynamic expansion by a few orders of magnitude up tothe density 1 × 1025 cm−3 with temperature in the range ofkeV–MeV [15]. The energy dissipation through x-ray emis-sion and ion response can be assumed negligible.

B. 3D PIC simulation results

2D benchmark simulations were performed using PICON-GPU code [30], which reproduce the primary results presentedabove. 3D simulations with both codes also support the ob-servation of wakefield excitation. The 3D simulation resultsby using PICONGPU code are shown in Fig. 6. For linearlypolarized laser field, the plasma wavelength, wakefield phasevelocity, fast electron temperature, and the energy gain re-main similar to 2D simulation. The longitudinal electric field,density perturbation, and electron energy cutoff are stronger.These are shown in Figs. 6(a)–6(f), where the one-to-one com-parison to 2D simulation is apparent. As expected, electroncrossing remains unaffected in the 3D geometry despite thepresence of a large transverse surface current [see Figs. 6(g)].This is evident through the transverse phase space diagram,px/(mc) in Fig. 6(i), which match the beam position of the Jx

component in Fig. 6(h). A small amount of pz/(mc) compo-nent also present inside the nanowire as shown in Fig. 6(j).This differs from the nanocluster interaction, where electronscirculating around the surface rather than oscillating throughthe structure [31,32]. On the other hand, the energy absorp-tion rate by electrons trapped in the wakefield at the initialirradiation phase is ∼0.1%. Despite the small conversion rate,the energy enhancement and wakefield penetration inside thenanowire outperform the flat target. It is worth mentioningthat for circularly polarized laser field, the electron crossingand J × B heating is ineffective and the wakefield excitationis strongly suppressed (see the SM for benchmark and 3Dsimulation results [25]).

To the best of our knowledge, these results provide clearevidence of particle-driven wakefield excitation in a soliddensity nanowire. Detailed investigation of the electron tra-jectories improves the understanding of electron transport inthe nanowire. A key finding was that the entering electronsupplied by the surrounding laser electric field assists a deeperwakefield propagation in the nanowire over the flat target. Thishas an important implication for deep energy penetration andsuggests an alternative mechanism for laser heating which

may be possible only for nanostructured materials. To opti-mize the electron acceleration in the nanostructure, conditionssuch as structure dimension and injection conditions demandinvestigation in detail. Making full use of the acceleratinggradient of ∼1 TeV m−1, electron energy gain up to 1 GeVmay be expected within the length of 1 mm.

IV. CONCLUSIONS

In summary, we have reported the wakefield generation in asolid density nanowire immediately following the interactionwith an intense laser pulse. The driving force of the wakefieldis identified to be the 2ωL electron bunches generated by theJ × B heating at the tip of the nanowire. The wakefield isoscillating at the plasma frequency and its amplitude can reach2.4 TV m−1. Electrons are subsequently injected and acceler-ated by the wakefield deep into the nanowire when the rightinitial conditions are met. In addition, the laser electric fieldnormal to the nanowire surface swings the electron acrossthe nanowire. We have shown that the electron oscillationamplitude is larger than the nanowire itself and the vacuumheating is not effective. Instead, these electrons act as drivebunch and have facilitated a deeper wakefield propagation intothe nanowire which results in 2.5× energy gain over a flattarget. These interplay open insights into the laser volumetricheating of nanostructure targets. The enhanced electron en-ergy gain will offer efficient x-ray and γ -ray sources whenthe supporting substrate is substituted by the high-Z materials[33]. The observation of such a large-amplitude wakefieldexcitation may motivate the development of plasma wakefieldacceleration in solid density plasma [34].

ACKNOWLEDGMENTS

J.F.O. thanks L. G. Huang for the fruitful discussion.P.G. acknowledges the support of the Romanian Ministry ofEducation and Research through the PN 19060105 and ELI-RO FLAP (ELI-RO-2017-27) projects. K.A.T. acknowledgesintriguing comments from A. Pukhov, Heinrich Heine Uni-versity Dusseldorf, Germany. This work was supported by theExtreme Light Infrastructure Nuclear Physics (ELI-NP) PhaseII, a project cofinanced by the Romanian Government andthe European Union through the European Regional Devel-opment Fund - the Competitiveness Operational Programme(1/07.07.2016, COP, ID 1334).

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